Answer
$x=-\dfrac{\ln2-1}{4}\approx0.076713$
Work Step by Step
$e^{1-4x}=2$
Apply $\ln$ to both sides of the equation:
$\ln e^{1-4x}=\ln2$
Take down the exponent $(1-4x)$ to multiply in front of its respective $\ln$:
$(1-4x)\ln e=\ln2$
Since $\ln e=1$, the equation becomes:
$1-4x=\ln2$
Solve for $x$:
$-4x=\ln2-1$
$x=-\dfrac{\ln2-1}{4}\approx0.076713$
